summer flood. The winter being less rainy than the summer, nothing particularly happens at the winter solstice, but that the frosts commonly set in more severely, with some quantity of snow, upon the ground.

OF THE ARTIFICIAL OR TERRESTRIAL HORIZON.

The brass circle, which may be slipped from pole to pole on the moveable meridian, has been already described. The circumference of it is divided into eight parts, to which are affixed the initial letters of the mariner's compass.

When the centre of it is set to any particular place, the situation of any other place is seen, with respect to that place; that is, whether they be east, west, north, or south of it.

It will, therefore, represent the horizon of that place.

We shall here use the artificial horizon, to shew why the sun, although he be always in one and the same place, appears to the inhabitants of the earth at different altitudes, and in different azimuths.

PROBLEM XVI. To exemplify the sun's altitude, as observed with an artificial horizon.

The altitude of the sun is greater or less, according as the line which goes from us to the sun is nearer to, or farther off, from our horizon.

Let the moveable circle be applied to any place,

as London, then will the horizon of London be thereby represented.

The sun is supposed, as before, to be in the zenith, that is, directly over the terrestrial globe. . If, then, from London, a line go vertically upwards, the sun will be seen at London in that line.

At sun-rising, when London is brought to the west edge of the broad paper circle, the supposed line will be parallel to the artificial horizon, and the sun will then be seen in the horizon.

As the globe is gradually turned from the west towards the east, the horizon will recede from that line which goes from London vertically upwards; so that the line in which the sun is seen gets further and further from the horizon; that is, the sun's altitude increases gradually.

When the horizon, and the line which goes from London vertically upwards, are arrived at the strong brass meridian, the sun is then at his greatest, or meridian altitude for that day, and the line and horizon are at the largest angle they can make with each other.

After this, the motion of the globe being continued, the angle between the artificial horizon and the line which goes from London vertically upwards continually decreases, until London arrives at the eastern edge of the broad paper circle; its horizon then becomes vertical again, and parallel to the line which goes vertically upwards. The sun will again appear in the horizon, and will set.

PROBLEM XVII. Of the sun's meridian altitude, at three different seasons.

Rectify the globe to the time of the winter solstice, by Problem xiv, and place the centre of the visible horizon on London.

When London is at the graduated edge of the strong brass meridian, the line which goes vertically upwards, makes an angle of about 15 degrees; this is the sun's meridian altitude at that season to the inhabitants of London.

If the globe be rectified to the times of equinox, by Problem xv, the horizon will be farther separated from the line which goes vertically upwards, and makes a greater angle therewith, it being about 38 degrees; this is the sun's meridian altitude at the time of equinox at London.

Again, rectify to the summer solstice by Problem xiii, and you will find the artificial horizon recede farther from the line which goes from London vertically upwards, and the angle it then makes, is about 62 degrees, which shews the sun's meridian altitude at the time of the summer solstice.

Hence, flows also the following arithmetical problem.

PROBLEM XVIII. To find the meridian altitude universally.

Add the sun's declination to the elevation of the

equator, if the latitude of the place, and the declination of the sun, are both on the same side.

If on contrary sides, subtract the declination from the elevation of the equator, and you obtain the sun's meridian altitude.

Thus, the elevation of the equator at London is

38

The sun's declination on the 20th of May 20

Their sum, the sun's meridian altitude that

day

Again, to the elevation of the equator at
London

28

8

58 36

38 28

Add the sun's greatest declination at the time of the summer solstice

The sum is the sun's greatest meridian altititude at London

- 61 57

PROBLEM XIX. Of the sun's azimuths, as compared with the artificial horizon.

The artificial horizon serves, also, to determine the sun's azimuths.

An azimuth of the sun is denominated from that point of the horizon, to which the sun, or a line going to the sun, is nearest.

Thus, if the sun, or a line going to the sun, be nearest the south-east point of the horizon, which

point is 45 degrees distant from the meridian, the sun's azimuth is an azimuth of 45 degrees, and the sun will appear in the south-east.

Imagine the sun, as we have done before, to be placed directly over the globe.

In which case, a line going to the sun from any place on the surface of the globe, will have a vertical direction, and will go from that place vertically upwards.

If, then, we apply the artificial horizon to any place, the point of this horizon, to which a vertical line is nearest, shews the sun's azimuth at that time.

It is observable, that the point of the horizon, to which such a vertical line is nearest, will be, at all times, that point which is most elevated.

To exemplify this, let the globe be in the position of a right sphere, and let the artificial horizon be applied to London.

When London is at the western edge of the broad paper circle, which situation represents the time when the sun appears to rise, the eastern point of the artificial horizon being then most elevated, shews that the sun at his rising is due east.

Turn the globe, till London comes to the eastern edge of the broad paper circle, then the western point of the artificial horizon will be most elevated, shewing that the sun sets due west.

Now, place the globe in the position of an oblique sphere; and, if London be brought to the eastern or western side of the broad paper circle, the ver